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International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 18, Pages 3005-3013
http://dx.doi.org/10.1155/IJMMS.2005.3005

On the fine spectrum of the generalized difference operator B(r,s) over the sequence spaces c0 and c

Bilâl Altay and Feyzı Başar

Matematik Eğitim Fakültesi, İnönü Üniversitesi, Malatya 44280, Turkey

Received 27 April 2005; Revised 15 July 2005

Copyright © 2005 Bilâl Altay and Feyzı Başar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We determine the fine spectrum of the generalized difference operator B(r,s) defined by a band matrix over the sequence spaces c0 and c, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operator Δ, and includes as other special cases the right shift and the Zweier matrices.